Subdivision + Solidify + Bridge Edge Loop
Your face orientation is causing this problem. To see face orientation you can check Face Orientation under Viewport Overlays tab. Blue is outside. Red is inside.

To solve this select your object and toggle to edit mode. Press a to select all. Then press Shift+n to Recalculate Outside. This fill flip normals that are inside-out. You can also select Mesh tab and from Normals select Recalculate Outside.